8-2a(a+2)=7+a

Solution for 8-2a(a+2)=7+a equation:

8-2a(a+2)=7+a

We move all terms to the left:

8-2a(a+2)-(7+a)=0

We add all the numbers together, and all the variables

-2a(a+2)-(a+7)+8=0

We multiply parentheses

-2a^2-4a-(a+7)+8=0

We get rid of parentheses

-2a^2-4a-a-7+8=0

We add all the numbers together, and all the variables

-2a^2-5a+1=0

a = -2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-2)·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*-2}=\frac{5-\sqrt{33}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-2}=\frac{5+\sqrt{33}}{-4}
$